A note on the vertical distribution of momentum transport in water waves

2015 ◽  
Vol 44 (4) ◽  
Author(s):  
Jerzy Kołodko ◽  
Gabriela Gic-Grusza
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Continuous Distribution ◽  
Classical Problem ◽  
Ocean Dynamics ◽  
Momentum Transport ◽  
Generalized Function ◽  
Dirac Delta ◽  
The Mean ◽  
Transport Flux

AbstractIn this paper, the classical problem of horizontal waveinduced momentum transport is analyzed once again. A new analytical approach has been employed to reveal the vertical variation of this transport in the Eulerian description.In mathematical terms, this variation is shown to have (after “smoothing out” the surface corrugation) the character of a generalized function (distribution) and is described by a classical function in the water depths and by an additional Dirac-delta-function component on the averaged free surface.In terms of physics, the considered variation consists of two entities: (i) a continuous distribution of the mean momentum transport flux density (tensorial radiation pressure) over the entire water column, and (ii) an additional momentum transport flux concentrated on the mean free surface level (tensorial radiation surface pressure). Simple analytical formulae describing this variation have been derived.This allowed a conventional expression to be derived, describing the depth-integrated excess of horizontal momentum flux due to the presence of waves (the so-called “radiation stress”), confirming to some extent the correctness of the whole analysis carried out.The results obtained may be important to the ocean dynamics, especially in view of their possible application in the field of hydrodynamics of wave-dominated coastal zones.

Cloaking a vertical cylinder via homogenization in the mild-slope equation

2016 ◽  
Vol 796 ◽  
Author(s):  
G. Dupont ◽  
S. Guenneau ◽  
O. Kimmoun ◽  
B. Molin ◽  
S. Enoch
Keyword(s):  
Free Surface ◽  
Conformal Mapping ◽  
Water Waves ◽  
Vertical Cylinder ◽  
Far Field ◽  
Physical Constraints ◽  
Mild Slope Equation ◽  
The Mean ◽  
Drift Force ◽  
Linear Water Waves

We describe a method to construct devices which allows a vertical rigid cylinder to be cloaked for any far-field observer in the case of linear water waves. An adaptation of parameters given by a geometric transform performed in the mild-slope equation is achieved via homogenization. The final device, which respects the physical constraints of the problem, is obtained with a conformal mapping. The result of this algorithm is a structure surrounding the vertical cylinder, composed of an annular region with varying bathymetry and with rigid vertical objects piercing the free surface. An approximate cloaking is achieved, which implies a reduction of the mean drift force acting on the cylinder.

scholarly journals On deep-sea water waves caused by a local disturbance on or beneath the surface

1915 ◽  
Vol 92 (635) ◽  
pp. 57-81 ◽  
Keyword(s):  
Free Surface ◽  
Deep Sea ◽  
Water Waves ◽  
Sea Water ◽  
Classical Problem ◽  
Finite Depth ◽  
Initial Disturbance ◽  
Integral Theorem ◽  
Local Disturbance ◽  
Deep Sea Water

The classical problem of waves produced in deep-sea water by a local disturbance of the free surface has been investigated by Prof. H. Lamb in a very able manner. He completed the theory of wave propagation in one dimension and in two horizontal dimensions when the initial disturbance is concentrated in the immediate neighbourhood of a line or a point, assuming that Fourier's double integral theorem can be applied in such a case. In this paper I venture to disturbance, followong Prof. Lamb's method, in cases where the initial disturbance is spread over a certain extent of the free surface; and, as an application of the general solution, I propose to treat the case in which the initial disturbing source is situated at a finite depth from the surface, i.e. where the surface wave is produced by an explosion like that of a mine under water.

Rankine and Fourier-Kochin Representation of Near-Field Ship Waves

2002 ◽  
Vol 46 (01) ◽  
pp. 63-79
Author(s):  
Francis Noblesse
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Near Field ◽  
Boundary Surface ◽  
Diffraction Radiation ◽  
Offshore Structure ◽  
Ship Waves ◽  
Time Harmonic ◽  
The Mean ◽  
Elementary Waves

New fundamental analytical representations of the near-held potential how that corresponds to a given how at a surface bounding a potential-how region are given for three classes of free-surface hows in deep water: diffraction-radiation of regular water waves by an offshore structure, steady ship waves, and time-harmonic ship waves (diffraction-radiation with forward speed). These near-held how representations, called Rankine and Fourier-Kochin representations, define the how in terms of distributions of Rankine singularities and Fourier-Kochin distributions of elementary waves over the boundary surface and its intersection with the mean free surface. The Rankine and Fourier-Kochin near-held how representations involve only simple ordinary functions. These how representations extend the previously given Fourier-Kochin representations of waves.

scholarly journals An alternative approach to study irrotational periodic gravity water waves

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Biswajit Basu ◽  
Calin I. Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Stagnation Points ◽  
Alternative Approach ◽  
New Formulation ◽  
Bounded Below ◽  
Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

scholarly journals Bound Coherent Structures Propagating on the Free Surface of Deep Water

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 115
Author(s):  
Dmitry Kachulin ◽  
Sergey Dremov ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Nonlinear Models ◽  
Ideal Incompressible Fluid ◽  
Equation Model ◽  
System Of Nonlinear Equations ◽  
Potential Flows ◽  
Deep Water Waves

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

Effective Power and Speed Loss of Underwater Vehicles in Close Proximity to Regular Waves

2017 ◽  
Author(s):  
Stefan Daum ◽  
Martin Greve ◽  
Renato Skejic
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Water Waves ◽  
Underwater Vehicles ◽  
Total Resistance ◽  
Wave Load ◽  
Regular Waves ◽  
Effective Power ◽  
Close Proximity ◽  
Deep Water Waves

The present study is focused on performance issues of underwater vehicles near the free surface and gives insight into the analysis of a speed loss in regular deep water waves. Predictions of the speed loss are based on the evaluation of the total resistance and effective power in calm water and preselected regular wave fields w.r.t. the non-dimensional wave to body length ratio. It has been assumed that the water is sufficiently deep and that the vehicle is operating in a range of small to moderate Froude numbers by moving forward on a straight-line course with a defined encounter angle of incident regular waves. A modified version of the Doctors & Days [1] method as presented in Skejic and Jullumstrø [2] is used for the determination of the total resistance and consequently the effective power. In particular, the wave-making resistance is estimated by using different approaches covering simplified methods, i.e. Michell’s thin ship theory with the inclusion of viscosity effects Tuck [3] and Lazauskas [4] as well as boundary element methods, i.e. 3D Rankine source calculations according to Hess and Smith [5]. These methods are based on the linear potential fluid flow and are compared to fully viscous finite volume methods for selected geometries. The wave resistance models are verified and validated by published data of a prolate spheroid and one appropriate axisymmetric submarine model. Added resistance in regular deep water waves is obtained through evaluation of the surge mean second-order wave load. For this purpose, two different theoretical models based on potential flow theory are used: Loukakis and Sclavounos [6] and Salvesen et. al. [7]. The considered theories cover the whole range of important wavelengths for an underwater vehicle advancing in close proximity to the free surface. Comparisons between the outlined wave load theories and available theoretical and experimental data were carried out for a submerged submarine and a horizontal cylinder. Finally, the effective power and speed loss are discussed from a submarine operational point of view where the mentioned parameters directly influence mission requirements in a seaway. All presented results are carried out from the perspective of accuracy and efficiency within common engineering practice. By concluding current investigations in regular waves an outlook will be drawn to the application of advancing underwater vehicles in more realistic sea conditions.

Varietal reactions of Trifolium subterraneum L. to Phaseolus virus 2 Pierce.

1954 ◽  
Vol 5 (4) ◽  
pp. 598 ◽  
Author(s):  
EM Hutton ◽  
JW Peak
Keyword(s):  
Trypan Blue ◽  
Continuous Distribution ◽  
Systemic Infection ◽  
Subterranean Clover ◽  
Trifolium Subterraneum ◽  
Epidermal Cells ◽  
Severe Strain ◽  
Resistant Varieties ◽  
Lethal Reaction ◽  
The Mean

A number of varieties of subterranean clover (Trifolium subterraneum L.) were tested with a severe strain of Phaseolus virus 2 Pierce. Northam First Early, Dwalganup, and Pink Flowered gave lethal necrotic reactions while the rest developed mottles and chlorosis of different degrees of intensity. Reductions in the mean fresh weights of plants of five subterranean clover varieties ranged from 26.1 to 76.7 per cent. Epidermal cells of mottled leaves contained irregular aggregates of viroplasts stained by treatment with phloxine-trypan blue. Viroplasts in young tip leaves did not stain if the plants were held at temperatures below 44.6°F while those in mature basal leaves were not so affected. The lethal-reactors Northam First Early, Dwalganup, and Pink Flowered were resistant in the field to Phaseolus virus 2. With hand inoculation in the glass-house an average of 10 per cent. of plants of these varieties remained free from systemic infection, whereas all the plants of mottle-reacting varieties became systemically infected. The virus had a discontinous distribution in plants of lethal-reactors, compared with a continuous distribution in those of mottle-reactors such as Mount Barker. The lethal reaction is heritable in a dominant fashion in most crosses, so that the development of desirable new virus- resistant varieties is possible.

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